EXAMPLE 11 Mean and standard error of

The National Institutes of Health reported that color blindness linked to the X chromosome afflicts 8% of men. Suppose we take a random sample of 100 men and let denote the proportion of men in the population who have color blindness linked to the X chromosome. Find and .

Solution

First, we note that this is a binomial experiment with and . Fact 5 tells us that ; that is, the sampling distribution of the sample proportion has a mean of . Fact 6 states that the standard error is